Question

Precalc help
An investor deposits $50 on the first day of each month in an account that pays 3% interest compounded monthly. What is the balance at the end of 2 years?

Answer 1

Have you considered calculating it?

i = 0.03 Annual Interest
j = i/12 = 0.0025 Monthly Interest
r = 1+j = 1.0025 Monthly Accumulation Factor

End of Month #1: 50r
End of Month #2: (50r+50)r = 50(r^2 + r)
End of Month #3: 50(r^3 + r^2 + r)
...
End of Month #24: 50(r^24 + r^23 + ... + r^3 + r^2 + r)

Your task is to add all that up!

Answer 2

Or here is a formula that doesn't require your adding up 2 years worth of calculations:

Answer 3

Thanks to both of you

Answer 4

Where do you think the formula came from? Learn how to add those up. WAY better than trying to figure out which formula to use. \(\huge{WAY}\) better.

Answer 5

Plus, it's important to note that the formula given is incorrect. That subtraction on the end should not be there.

Answer 6

My formula IS correct.
Using my formula:
rate = .03/12 = .0025 n=24 months

Total = Mnth Amt * ([(1+r)^(n+1)-1]/r) - Mnth Amt
Total = 50 * (((1.0025)^25/.0025)-1) - Mnth Amt
Total = 50 * (1.06441143687263 -1)/.0025) -Mnth Amt
Total = 50 * (.06441143687263 /.0025) - Mnth Amt
Total = (50 * 25.764574749053) -50
Total = 1,288.2287374527 - 50
Total = 1,238.23
Calculator located here: https://www.jaxmetro.org/calc/fv_multi.html
says total is 1,238.22
Okay, I'm a penny off.
I guess my formula needs re-writing (even though it is correct).
I'll re-write it as (1+r)^n instead of (n+1) and eliminate the (-Mnth Amt)

Answer 7

Can't argue the result. Your "Total #2" is written incorrectly. I'm not sure why you would ever want to write it that way. Anyway...